Algebra Examples

${(\frac{4}{9} y^{2} - \frac{1}{4})}^{2}$

Step 1

Combine fractions.

Tap for more steps...

Step 1.1

Combine $\frac{4}{9}$ and $y^{2}$ .

${(\frac{4 y^{2}}{9} - \frac{1}{4})}^{2}$

Step 1.2

Rewrite ${(\frac{4 y^{2}}{9} - \frac{1}{4})}^{2}$ as $(\frac{4 y^{2}}{9} - \frac{1}{4}) (\frac{4 y^{2}}{9} - \frac{1}{4})$ .

$(\frac{4 y^{2}}{9} - \frac{1}{4}) (\frac{4 y^{2}}{9} - \frac{1}{4})$

Step 2

Expand $(\frac{4 y^{2}}{9} - \frac{1}{4}) (\frac{4 y^{2}}{9} - \frac{1}{4})$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$\frac{4 y^{2}}{9} (\frac{4 y^{2}}{9} - \frac{1}{4}) - \frac{1}{4} (\frac{4 y^{2}}{9} - \frac{1}{4})$

Step 2.2

Apply the distributive property.

$\frac{4 y^{2}}{9} \cdot \frac{4 y^{2}}{9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} (\frac{4 y^{2}}{9} - \frac{1}{4})$

Step 2.3

Apply the distributive property.

$\frac{4 y^{2}}{9} \cdot \frac{4 y^{2}}{9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Combine.

$\frac{4 y^{2} (4 y^{2})}{9 \cdot 9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.2

Multiply $y^{2}$ by $y^{2}$ by adding the exponents.

Tap for more steps...

Step 3.1.2.1

Move $y^{2}$ .

$\frac{4 (y^{2} y^{2}) \cdot 4}{9 \cdot 9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{4 y^{2 + 2} \cdot 4}{9 \cdot 9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.2.3

Add $2$ and $2$ .

$\frac{4 y^{4} \cdot 4}{9 \cdot 9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.3

Multiply $4$ by $4$ .

$\frac{16 y^{4}}{9 \cdot 9} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.4

Multiply $9$ by $9$ .

$\frac{16 y^{4}}{81} + \frac{4 y^{2}}{9} (- \frac{1}{4}) - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.5

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.1.5.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{16 y^{4}}{81} + \frac{4 y^{2}}{9} \cdot \frac{- 1}{4} - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.5.2

Factor $4$ out of $4 y^{2}$ .

$\frac{16 y^{4}}{81} + \frac{4 (y^{2})}{9} \cdot \frac{- 1}{4} - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.5.3

Cancel the common factor.

$\frac{16 y^{4}}{81} + \frac{4 y^{2}}{9} \cdot \frac{- 1}{4} - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.5.4

Rewrite the expression.

$\frac{16 y^{4}}{81} + \frac{y^{2}}{9} \cdot - 1 - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.6

Combine $\frac{y^{2}}{9}$ and $- 1$ .

$\frac{16 y^{4}}{81} + \frac{y^{2} \cdot - 1}{9} - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.7

Move $- 1$ to the left of $y^{2}$ .

$\frac{16 y^{4}}{81} + \frac{- 1 \cdot y^{2}}{9} - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.8

Move the negative in front of the fraction.

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - \frac{1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.9

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.1.9.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} + \frac{- 1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.9.2

Factor $4$ out of $4 y^{2}$ .

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} + \frac{- 1}{4} \cdot \frac{4 (y^{2})}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.9.3

Cancel the common factor.

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} + \frac{- 1}{4} \cdot \frac{4 y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.9.4

Rewrite the expression.

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - 1 \frac{y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.10

Rewrite $- 1 \frac{y^{2}}{9}$ as $- \frac{y^{2}}{9}$ .

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - \frac{y^{2}}{9} - \frac{1}{4} (- \frac{1}{4})$

Step 3.1.11

Multiply $- \frac{1}{4} (- \frac{1}{4})$ .

Tap for more steps...

Step 3.1.11.1

Multiply $- 1$ by $- 1$ .

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - \frac{y^{2}}{9} + 1 (\frac{1}{4}) \frac{1}{4}$

Step 3.1.11.2

Multiply $\frac{1}{4}$ by $1$ .

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - \frac{y^{2}}{9} + \frac{1}{4} \cdot \frac{1}{4}$

Step 3.1.11.3

Multiply $\frac{1}{4}$ by $\frac{1}{4}$ .

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - \frac{y^{2}}{9} + \frac{1}{4 \cdot 4}$

Step 3.1.11.4

Multiply $4$ by $4$ .

$\frac{16 y^{4}}{81} - \frac{y^{2}}{9} - \frac{y^{2}}{9} + \frac{1}{16}$

Step 3.2

Subtract $\frac{y^{2}}{9}$ from $- \frac{y^{2}}{9}$ .

$\frac{16 y^{4}}{81} - 2 \frac{y^{2}}{9} + \frac{1}{16}$

Step 4

Simplify each term.

Tap for more steps...

Step 4.1

Combine $- 2$ and $\frac{y^{2}}{9}$ .

$\frac{16 y^{4}}{81} + \frac{- 2 y^{2}}{9} + \frac{1}{16}$

Step 4.2

Move the negative in front of the fraction.

$\frac{16 y^{4}}{81} - \frac{2 y^{2}}{9} + \frac{1}{16}$